The square of a subcubic planar graph without a 5-cycle is 7-choosable
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908741076516864 |
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| author | Kim, Seog-Jin Lian, Xiaopan Nakamoto, Atsuhiro Ozeki, Kenta |
| author_facet | Kim, Seog-Jin Lian, Xiaopan Nakamoto, Atsuhiro Ozeki, Kenta |
| contents | The square of a graph $G$, denoted $G^2$, has the same vertex set as $G$ and has an edge between two vertices if the distance between them in $G$ is at most $2$. Thomassen [12] showed that $χ(G^2) \leq 7$ if $G$ is a subcubic planar graph. A natural question is whether $χ_{\ell}(G^2) \leq 7$ or not if $G$ is a subcubic planar graph. Recently Kim and Lian [11] showed that $χ_{\ell}(G^2) \leq 7$ if $G$ is a subcubic planar graph of girth at least 6. And Jin, Kang, and Kim [10] showed that $χ_{\ell}(G^2) \leq 7$ if $G$ is a subcubic planar graph without 4-cycles and 5-cycles. In this paper, we show that the square of a subcubic planar graph without 5-cycles is 7-choosable, which improves the results of [10] and [11]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24536 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The square of a subcubic planar graph without a 5-cycle is 7-choosable Kim, Seog-Jin Lian, Xiaopan Nakamoto, Atsuhiro Ozeki, Kenta Combinatorics 05C15 The square of a graph $G$, denoted $G^2$, has the same vertex set as $G$ and has an edge between two vertices if the distance between them in $G$ is at most $2$. Thomassen [12] showed that $χ(G^2) \leq 7$ if $G$ is a subcubic planar graph. A natural question is whether $χ_{\ell}(G^2) \leq 7$ or not if $G$ is a subcubic planar graph. Recently Kim and Lian [11] showed that $χ_{\ell}(G^2) \leq 7$ if $G$ is a subcubic planar graph of girth at least 6. And Jin, Kang, and Kim [10] showed that $χ_{\ell}(G^2) \leq 7$ if $G$ is a subcubic planar graph without 4-cycles and 5-cycles. In this paper, we show that the square of a subcubic planar graph without 5-cycles is 7-choosable, which improves the results of [10] and [11]. |
| title | The square of a subcubic planar graph without a 5-cycle is 7-choosable |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2512.24536 |